Variable Selection in Regression Using Maximal Correlation and Distance Correlation

• Activity Number: 191
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Deniz Yenigun*+ and Maria L. Rizzo
• Companies: Bilkent University and Bowling Green State University
• Keywords: variable selection ; maximal correlation ; distance correlation

Abstract

In most of the regression problems the first task is to select the most influential predictors explaining the response, and removing the others from the model. These problems are usually referred to as the variable selection problems in the statistical literature, and numerous methods have been proposed. In this study we propose two stepwise variable selection methods based on two strong dependence measures, namely, maximal correlation and distance correlation. Both methods are easy to implement and they perform well. We illustrate the performance of the proposed methods via simulations, and compare them with two benchmark methods, stepwise AIC and lasso. In several cases all four methods turned out to be comparable. In the presence of nonlinear or uncorrelated dependencies, we observed that our methods may be favorable. An application of the proposed methods to a real financial data set is considered.